# POLYGONAL PRODUCTS OF RESIDUALLY FINITE GROUPS

• Wong, Kok-Bin (Institute of Mathematical Sciences University of Malaya) ;
• Wong, Peng-Choon (Institute of Mathematical Sciences University of Malaya)
• Published : 2007.02.28
• 80 6

#### Abstract

A group G is called cyclic subgroup separable for the cyclic subgroup H if for each $x\;{\in}\;G{\backslash}H$, there exists a normal subgroup N of finite index in G such that $x\;{\not\in}\;HN$. Clearly a cyclic subgroup separable group is residually finite. In this note we show that certain polygonal products of cyclic subgroup separable groups amalgamating normal subgroups are again cyclic subgroup separable. We then apply our results to polygonal products of polycyclic-by-finite groups and free-by-finite groups.

#### Keywords

subgroup separable;polygonal products;polycyclic-by-finite groups;free-by-finite groups;abelian groups

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#### Cited by

1. The Weakly Potency of Certain HNN Extensions of Nilpotent Groups vol.21, pp.04, 2014, https://doi.org/10.1142/S1005386714000637
2. CYCLIC SUBGROUP SEPARABILITY OF CERTAIN GRAPH PRODUCTS OF SUBGROUP SEPARABLE GROUPS vol.50, pp.5, 2013, https://doi.org/10.4134/BKMS.2013.50.5.1753